Axisymmetric and swirling jets are generic flows that characterize many natural and man-made flows. These include cylindrical shear layer/mixing layer flows, aircraft jets and wakes, shedding of leading edge and wing tip vortices, tornadoes, astrophysical plasma flows and flows in mechanical devices such as supersonic combustion chambers and cyclone separators. These and other applications have resulted in a high level of interest in the stability of axisymmetric and swirling jets. To date, the majority of studies on stability of axisymmetric and swirling jets have been completed under the assumption of steady flow in both axial and azimuthal (swirl) directions. Yet, flows such as the ones mentioned above can have an inherent unsteadiness. Moreover, such unsteadiness can be used to control stability and thus flow characteristics in axisymmetric and swirling jets. In this work effects of periodic variations on the temporal stability of axisymmetric and swirling jets is examined. The unsteadiness is introduced in the former as a periodic variation of the axial velocity component of the flow, and in the latter as a periodic variation of the azimuthal (swirl) velocity component of the flow. The temporal linear hydrodynamic stability of both steady inviscid axisymmetric and swirling jets is reviewed. An analytical dispersion relation is obtained in both cases and solved numerically. In the case of the steady axisymmetric jet, growth rate and celerity of unstable axisymmetric and helicalmodes are determined as functions of axial wavenumber. Results show that the inviscid axisymmetric jet is unstable to all values of axisymmetric and helical modes. In the case of the steady swirling jet, growth rate and celerity of axisymmetric modes are determined as functions of the axial wavenumber and swirl number. Results show that the inviscid swirling jet is unstable to all values of axial and azimuthal wavenumber, however, it is shown that increasing the swirl decreases the growth rate and increases the celerity of axisymmetric disturbances. The effects of periodic variations on the stability of a mixing layer is also reviewed. Results show that when the instability time scale is much smaller than the mean time scale a transformation of the time variable may be taken that, when the quasi-steady approach works, will reduce the unsteady field to that of the corresponding steady field in the new time scale. The price paid for this transformation, however, is a modulation of the amplitude and phase of the unsteady modes. Extending the results from the unsteady mixing layer, the stability of a periodically unsteady inviscid axisymmetric jet is considered. An analytical dispersion relation is obtained and results show that for the unsteady inviscid axisymmetric jet, the quasi-steady approach works. Following this, the stability of a periodically unsteady swirling jet is considered and an analytical dispersion relation is obtained. It is shown that for the unsteady inviscid swirling jet, the quasi-steady approach does not work. Resulting modulations of unsteady modes are shown via a numerical solution to the unsteady dispersion relation. In both cases, using established results for unsteady mixing layers, these results are substantiated analytically by showing that the unsteady axisymmetric jet can be reduced the the exact equational form of the steady axisymmetric jet in a new time scale, whereas the unsteady swirling jet cannot. / Master of Science

Previous research has shown that expected market returns vary over time and that this variation can be predicted by variables such as dividend yields and book-to-market ratios (Fama and French (1989); Campbell and Thompson (2008)). Further, macroeconomic variables affect asset returns (Flannery and Protopapadikas (2002)). We investigate whether the investment decisions of mutual fund investors incorporate information about future stock returns contained in predictive and macroeconomic variables. If investors incorporate this information, then variation in flows should be related to that in predictive variables and macroeconomic variables. Using quarterly flow data from 1951Q4 to 2007Q4, we find that both predictive and macroeconomic variables have a relatively small impact on flows. Our results suggest that fund investors, as a group, fail to adequately incorporate the information contained in these variables. Existing literature documents that (i) an asymmetric low-performance relationship creates an incentive for managers to extract rents from shareholders, and (ii) managers respond to such incentives by strategically altering portfolio risk. Using the semiparametric regression model proposed by Chevalier and Ellison (1997), we show that the flow-performance relationship has become linear in recent years (2000-2009) and fund managers no longer respond to such incentives. Fund managers, however, change portfolio risk in response to past performance; such changes have a positive impact on fund performance and are indicative of a better alignment of interests between managers and shareholders. / Ph. D.

Laboratory experiments were conducted to investigate the effect of low relative depth and high Froude number on the dimensionless critical shear stress (Shields parameter). Spherical particles of four different densities and an 8mm diameter were used as movable test material. The relative depth ranged from 2 to 12 and the Froude number ranged from 0.36 to 1.29. The results show that the traditional Shields diagram cannot be used to predict the incipient motion of coarse sediment particles when the relative depth is below 10 and the Froude number is above 0.5, approximately. Experiments using glass balls, whose density is almost identical to that of natural gravel, show that the Shields parameter can be twice as large in shallow flows than in deep flows. The results also show that the Shields parameter is dependent on the density of the particles. Data obtained from other studies support the findings of the present work. These findings can result in significant cost savings for riprap. Additionally, velocity profiles using a laser-Doppler velocimeter (LDV) were taken for the glass ball incipient motion experiments. The purpose of this was to study possible changes in the velocity distribution with decreasing relative depth and increasing Froude number. The results show that the von Karman and integral constants in the law of the wall do not change in the range of relative depths and Froude numbers tested. / Master of Science

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In this study the complete four dimensional space time correlation function was measured in the wake of an untripped circular cylinder at a Reynolds number of 60 000. This correlation serves as the complete inflow boundary condition for an open rotor ingesting inhomogeneous turbulence. An important aspect of the turbulence ingestion problem is understanding how different inflow boundary conditions effect the sound produced by a rotor. In the present study the turbulence structure of two plane wakes were compared. Measurements completed by a previous study in the wake of a NACA 0012 airfoil were compared with the measurements completed by the present study in the wake of a cylinder. The mean flows of both plane wakes were found to be very similar, however the Reynolds stress profiles show that the cylinder wake is substantially more turbulent. The structures of the two-point correlation function in each wake are also similar, although the cylinder wake had greater maximum correlation values and was correlated at greater separations. The two-point correlation was used along with proper orthogonal decomposition to compute the average instantaneous velocity fields of both wake flows. These velocity fields represent the average eddy structures present in each wake flow. The eddy structure comparisons show that the structures in the cylinder wake are larger and better correlated at longer time delays. / Master of Science / Any fan or propeller that ingests any unsteady flow will produce noise. This is especially important in propeller aircraft and marine vehicles where turbulence is generated from appendages on the vehicle’s body. This self-generated turbulence travels downstream and is eventually drawn into the propeller and produces noise. The broad study that the present work is a part of is concerned with understanding this ingestion noise problem so that the interaction can be better modeled and the sound produced can be predicted. To predict the sound produced by a fan or propeller ingesting turbulence, detailed information about the inflow condition is needed. In the present study the turbulence structure of the wake shed by a circular cylinder at 20 meters per second. The two-point velocity correlation in the wake serves as the complete inflow condition for the turbulence ingestion problem. The structure of the cylinder wake inflow condition was compared with the structure of an airfoil wake to evaluate how the differences in the two flows would influence the sound produced by a rotor ingesting the two conditions. The two flows were found to be quite similar in the mean flow. The cylinder wake was found to be significantly more turbulent than the airfoil wake and was correlated over greater distances. This suggests that the structures in the cylinder wake are larger and remain coherent longer than those in the airfoil wake. The average instantaneous velocity fields were estimated in both wake flows and showed that the structures in the cylinder wake were significantly different from the structures in the airfoil wake. These flow structure comparisons show why the differences seen in the turbulence profiles and two-point correlations exist.

Yes / This study examines experimentally and for the first time the effect of reduced air pressure on dynamic wetting. The purpose is to assess the role of air viscosity on dynamic wetting failure which hitherto has been speculated on but not measured. In this paper we used dip coating as the model experimental flow and report data on air entrainment velocity Vae we measured with a series of silicone oils in a range of viscosities in a vacuum chamber where the pressure can be reduced from atmospheric down to a few mbar when the mean molecular free path of air is large and air ceases to have a viscosity. To complement earlier work, we carried out the experiments with a range of substrates of varying roughness. The substrates were chosen so that for each one, their two sides differ in roughness. This enables simultaneous comparative observation of their wetting performance and reduces the experimental error in assessing the role of roughness. The data presented here capture the effects of viscosity, roughness and air pressure but the important result of this study is that Vae can be increased considerably (exponentially) when the pressure is reduced with the suggestion that Vae approaches infinity as pressure approaches zero. In other words, the role of the surrounding air viscosity is important in dynamic wetting. The data from this study have significant implication to the fundamental understanding of dynamic wetting. Indeed they form the missing data link to fully understand this phenomenon. The data presented in this work also confirm the complex role of roughness, in that it can increase or decrease the air entrainment speed depending on the value on the viscosity of the coating solution. The results presented in this paper are very useful in practice as they imply that if one chooses carefully roughness one can coat viscous formulation at unexpectedly very high speeds with a moderate vacuum (50 mbar typically).

Yes / The coating flow examined here, labelled angled dip coating, is that where a substrate enters a pool of liquid forming an angle ß with the vertical so that it intersects the liquid along a wetting line which is not perpendicular to the direction of its motion. This flow situation is distinctly different from that where the substrate, inclined in the other dimension by the so-called angle of entry ¿, intersects the liquid surface perpendicularly to its motion. Experiments were carried out with various liquids to determine the effect of ß on the substrate velocity at which air is entrained into the liquid. It was observed that as this angle departs from zero, air entrainment is delayed to higher speeds. The data show that the speed which is relevant to air entrainment is not the velocity of the substrate itself but its component normal to the wetting line. This result has important practical implications and suggests that this fundamental principle is also applicable to other coating flows.

Yes / This study assesses experimentally the role of gas viscosity in controlling the minimum film thickness in slot coating in both the slot over roll and tensioned web modes. The minimum film thickness here is defined with respect to the onset of air entrainment rather than rivulets, the reason being that rivulets are an extreme form of instabilities occurring at much higher speeds. The gas viscosity effects are simulated experimentally by encasing the coaters in a sealed gas chamber in which various gases can be admitted. An appropriate choice of two gases was used to compare performances: air at atmospheric pressure and helium at sub-ambient pressure (25mbar), which we establish has a significantly lower “thin film” viscosity than atmospheric air. A capacitance sensor was used to continuously measure the film thickness on the web, which was ramped up in speed at a fixed acceleration whilst visualizations of the film stability were recorded through a viewing port in the chamber. The data collected show clearly that by coating in rarefied helium rather that atmospheric air we can reduce the minimum film thickness or air/gas entrainment low-flow limit. We attribute this widening of the stable coating window to the enhancement of dynamic wetting that results when the thin film gas viscosity is reduced. These results have evident practical significance for slot coating, the coating method of choice in many new technological applications, but it is their fundamental merit which is new and one that should be followed with further data and theoretical underpinning.

No / This study assesses experimentally the role of gas dissolution in gas entrainment which hitherto has been speculated on but not measured. In this paper, we used dip coating as the model experimental flow and performed the experiments with a dip coater encased in a vacuum chamber in which we admitted various gases. An appropriate choice of gases (air, carbon dioxide and helium) coupled with low pressure conditions from atmospheric down to 75 mbar enables us to test whether gas solubility is a key determinant in gas entrainment. The data presented here track the evolution in time of the size of bubbles of gas entrained in the liquid (silicone oil) which we observed to always occur at a critical speed, immediately after the dynamic wetting line breaks from a straight line into a serrated line with tiny vees the downstream apices of which are the locations from which the bubbles stream out. The results suggest that permeability combining solubility and diffusivity as a single parameter dictates the rate of dissolution when at atmospheric pressure. Helium, despite its comparatively sluggish rate of dissolution/growth into silicone oil was observed to have a more enhanced gas entrainment speed than air and carbon dioxide. Thus, the hypothetical contention from previous work (Miyamoto and Scriven, 1982) that gas can be entrained as a thin film which breaks into bubbles before dynamic wetting failure occurs is not realised, at least not in dip coating. The data presented here reinforce recent work by Benkreira and Ikin (2010) that thin film gas viscosity is the critical factor, over-riding dissolution during gas entrainment. This finding is fundamentally important and new and provides the experimental basis needed to develop and underpin new models for gas entrainment in coating flows.

This dissertation seeks to advance the modeling of network flows over time for the purposes of improving evacuation planning. The devastation created by Hurricanes Katrina and Rita along the Gulf Coast of the United States in 2005 have recently emphasized the need to improve evacuation modeling and planning. The lessons learned from these events, and similar past emergencies, have highlighted the problem of congestion on the interstate and freeways during an evacuation. The intent of this research is to develop evacuation demand management strategies that can reduce congestion, delay, and ultimately save lives during regional evacuations. The primary focus of this research will concern short-notice evacuations, such as hurricane evacuations, conducted by automobiles. Additionally, this dissertation addresses some traffic flow and optimization deficiencies concerning the modeling of congested network flows. This dissertation is a compilation of three manuscripts. Chapters 3 and 4 examine modeling network flows over time with congestion. Chapter 3 demonstrates the effects of congestion on flows using a microscopic traffic simulation software package, INTEGRATION. The flow reductions from the simulation are consistent with those found in several empirical studies. The simulation allows for the examination of the various contributing factors to the flow reductions caused by congestion, including level of demand, roadway geometry and capacity, vehicle dynamics, traffic stream composition, and lane changing behavior. Chapter 4 addresses some of the modeling and implementation issues encountered in evacuation planning and presents an improved modeling framework that reduces network flows due to congestion. The framework uses a cell-based linear traffic flow model within a mixed integer linear program (MILP) to model network flows over time in order to produce sets of decisions for use within an evacuation plan. The traffic flow model is an improvement based upon the Cell Transmission Model (CTM) introduced in Daganzo (1994) and Daganzo (1995) by reducing network flows due to congestion. The flow reductions are calibrated according to the traffic simulation studies conducted in Chapter 3. The MILP is based upon the linear program developed in Ziliaskopoulos (2000); however, it eliminates the "traffic holding" phenomenon where it cannot be implemented realistically within a transportation network. This phenomenon is commonly found in mathematical programs used for dynamic traffic assignment where the traffic is unrealistically held back in order to determine an optimum solution. Lastly, we propose additional constraints for the MILP that improve the computational performance by over 90%. These constraints exploit the relation of the binary variables based on the network topology. Chapter 5 applies the improved modeling framework developed in Chapter 4 to implement a demand management strategy called group-level staging -- the practice of evacuating different groups of evacuees at different times in order to reduce the evacuation duration. This chapter evaluates the benefits of group-level staging, as compared to the current practice of simultaneous evacuation, and explores the behavior of the modeling framework under various objective functions. / Ph. D.